Total Dilations
| dc.creator | Bourin, Jean-Christophe | |
| dc.date | 2002-11-22 | |
| dc.date.accessioned | 2026-07-07T04:53:12Z | |
| dc.date.available | 2026-07-07T04:53:12Z | |
| dc.description | (1) Let $A$ be an operator on a space ${\cal H}$ of even finite dimension. Then for some decomposition ${\cal H}={\cal F}\oplus{\cal F}^{\perp}$, the compressions of $A$ onto ${\cal F}$ and ${\cal F}^{\perp}$ are unitarily equivalent. (2) Let $\{A_j\}_{j=0}^n$ be a family of strictly positive operators on a space ${\cal H}$. Then, for some integer $k$, we can dilate each $A_j$ into a positive operator $B_j$ on $\oplus^k{\cal H}$ in such a way that: (i) The operator diagonal of $B_j$ consists of a repetition of $A_j$. (ii) There exist a positive operator $B$ on $\oplus^k{\cal H}$ and an increasing function $f_j : (0,\infty)\longrightarrow(0,\infty)$ such that $B_j=f_j(B)$. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0211359 | |
| dc.identifier | http://arxiv.org/abs/math/0211359 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65756 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47A20 | |
| dc.title | Total Dilations | |
| dc.type | text |